Problem: Rewrite as a simplified fraction. ${2.7\overline{1} = {?}}$
Explanation: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 271.1111...\\ 10x &= 27.1111...\end{align*}}$ Subtracting the two equations, we have: ${90x = 244}$ ${x = \dfrac{244}{90}} $ ${x = \dfrac{122}{45}} \text{or} {2 \dfrac{32}{45}}$